How many moles of oxygen must be placed in a 3.00 L container to exert a pressure of 2.00 atm at [tex]$25.0^{\circ} C$[/tex]?
Formula: [tex]$P V=n R T(R=0.0821 L \cdot atm / mol \cdot K )$[/tex]
Which variables are given?
pressure
volume
temperature
moles
Answer (1)
Convert the temperature from Celsius to Kelvin: T ( K ) = 25.0 + 273.15 = 298.15 K .
Use the ideal gas law equation: P V = n RT .
Rearrange the equation to solve for n: n = RT P V .
Substitute the given values and calculate: n = ( 0.0821 ) ( 298.15 ) ( 2.00 ) ( 3.00 ) ≈ 0.245 mol .
The number of moles of oxygen is 0.245 mol .
Explanation
Problem Analysis We are given the pressure, volume, and temperature of a gas, and we need to find the number of moles. We will use the ideal gas law to solve for the number of moles.
Convert Celsius to Kelvin First, we need to convert the temperature from Celsius to Kelvin. The formula for converting Celsius to Kelvin is: T ( K ) = T ( ∘ C ) + 273.15 So, we have: T ( K ) = 25.0 + 273.15 = 298.15 K
State the Ideal Gas Law and Rearrange Now, we can use the ideal gas law to find the number of moles (n). The ideal gas law is: P V = n RT Where:
P is the pressure (in atm)
V is the volume (in L)
n is the number of moles
R is the ideal gas constant (0.0821 L atm / (mol K))
T is the temperature (in K) We are given:
P = 2.00 atm
V = 3.00 L
R = 0.0821 L atm / (mol K)
T = 298.15 K We need to solve for n. Rearranging the ideal gas law equation to solve for n, we get: n = RT P V
Calculate the Number of Moles Now, we can plug in the given values and calculate the number of moles: n = ( 0.0821 mol ⋅ K L ⋅ atm ) ( 298.15 K ) ( 2.00 atm ) ( 3.00 L ) n = 24.511615 6.00 ≈ 0.245 mol
Final Answer Therefore, the number of moles of oxygen required is approximately 0.245 moles.
Examples
Understanding the number of moles of a gas is crucial in various real-world applications. For example, in scuba diving, knowing the number of moles of oxygen in a tank helps divers calculate how long they can stay underwater at a certain depth. Similarly, in chemical reactions, accurately determining the number of moles of reactants is essential for predicting the amount of product formed. In the food industry, modified atmosphere packaging (MAP) adjusts the gas composition within a package to extend the shelf life of perishable foods. Knowing the number of moles of each gas component ensures optimal preservation.
